Tree-structured statistical modeling via convex optimization

James Saunderson, Venkat Chandrasekaran, Pablo A. Parrilo, Alan S. Willsky

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)

Abstract

We develop a semidefinite-programming-based approach to stochastic modeling with multiscale autoregressive (MAR) processes-a class of stochastic processes indexed by the vertices of a tree. Given a tree and the covariance matrix of the variables corresponding to the leaves of the tree, our procedure aims to construct an MAR process with small state dimensions at each vertex that approximately realizes the given covariance at the leaves. Our method does not require prior specification of the state dimensions at each vertex. Furthermore, we establish a large class of MAR processes for which, given only the index tree and the leaf covariance of the process, our method can recover a parametrization that matches the leaf-covariance and has the correct state dimensions. Finally we demonstrate, using synthetic examples, that given i.i.d. samples of the leaf variables our method can recover the correct state dimensions of an underlying MAR process.

Original languageEnglish
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Subtitle of host publicationOrlando, Florida, USA, 12-15 December, 2011, [Proceedings]
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages2883-2888
Number of pages6
Volume1-12
ISBN (Print)9781612848006
DOIs
Publication statusPublished - 2011
Externally publishedYes
EventIEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011 - Hilton Orlando Bonnet Creek, Orlando, United States of America
Duration: 12 Dec 201115 Dec 2011
Conference number: 50th
http://www.ieeecss.org/CAB/conferences/cdcecc2011/cfp.php
https://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=15803

Conference

ConferenceIEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011
Abbreviated titleCDC-ECC 2011
CountryUnited States of America
CityOrlando
Period12/12/1115/12/11
Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Internet address

Cite this